LMFDB - Group of Dirichlet characters of modulus 520

sage:H = DirichletGroup(520)

pari:g = idealstar(,520,2)

Character group

sage:G.order() pari:g.no
Order	=	192
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{12}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{520}(391,\cdot)$, $\chi_{520}(261,\cdot)$, $\chi_{520}(417,\cdot)$, $\chi_{520}(41,\cdot)$

First 32 of 192 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{520}(1,\cdot)$	520.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{520}(3,\cdot)$	520.cm	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{520}(7,\cdot)$	520.cx	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{520}(9,\cdot)$	520.cb	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{520}(11,\cdot)$	520.cg	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{520}(17,\cdot)$	520.cr	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{520}(19,\cdot)$	520.cz	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{520}(21,\cdot)$	520.r	4	no	$-1$	$1$	$-1$	$-i$	$1$	$i$	$-1$	$-i$	$i$	$-1$	$-1$	$-1$
$\chi_{520}(23,\cdot)$	520.cn	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{520}(27,\cdot)$	520.be	4	no	$1$	$1$	$-i$	$-i$	$-1$	$1$	$i$	$-1$	$-1$	$i$	$i$	$1$
$\chi_{520}(29,\cdot)$	520.bv	6	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{520}(31,\cdot)$	520.s	4	no	$1$	$1$	$-1$	$-i$	$1$	$-i$	$-1$	$i$	$i$	$1$	$-1$	$1$
$\chi_{520}(33,\cdot)$	520.cw	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{520}(37,\cdot)$	520.cj	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{520}(41,\cdot)$	520.ch	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{520}(43,\cdot)$	520.cs	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{520}(47,\cdot)$	520.v	4	no	$-1$	$1$	$i$	$-1$	$-1$	$i$	$-i$	$i$	$-i$	$-i$	$-i$	$-1$
$\chi_{520}(49,\cdot)$	520.bz	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{520}(51,\cdot)$	520.o	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$
$\chi_{520}(53,\cdot)$	520.ba	4	no	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$-i$	$1$	$-1$	$i$	$i$	$1$
$\chi_{520}(57,\cdot)$	520.w	4	no	$1$	$1$	$-i$	$-1$	$-1$	$i$	$-i$	$i$	$i$	$i$	$i$	$-1$
$\chi_{520}(59,\cdot)$	520.cz	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{520}(61,\cdot)$	520.by	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{520}(63,\cdot)$	520.ck	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{520}(67,\cdot)$	520.ci	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{520}(69,\cdot)$	520.bp	6	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{520}(71,\cdot)$	520.da	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{520}(73,\cdot)$	520.w	4	no	$1$	$1$	$i$	$-1$	$-1$	$-i$	$i$	$-i$	$-i$	$-i$	$-i$	$-1$
$\chi_{520}(77,\cdot)$	520.bg	4	yes	$-1$	$1$	$i$	$-i$	$-1$	$1$	$i$	$-1$	$1$	$-i$	$-i$	$1$
$\chi_{520}(79,\cdot)$	520.n	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{520}(81,\cdot)$	520.q	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{520}(83,\cdot)$	520.x	4	yes	$-1$	$1$	$i$	$-1$	$-1$	$i$	$i$	$i$	$-i$	$i$	$-i$	$1$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$520$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{12}\)
Order	$192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{520}(1,\cdot)\)	520.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{520}(3,\cdot)\)	520.cm	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{520}(7,\cdot)\)	520.cx	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{520}(9,\cdot)\)	520.cb	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{520}(11,\cdot)\)	520.cg	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{520}(17,\cdot)\)	520.cr	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{520}(19,\cdot)\)	520.cz	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{520}(21,\cdot)\)	520.r	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{520}(23,\cdot)\)	520.cn	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{520}(27,\cdot)\)	520.be	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(1\)
\(\chi_{520}(29,\cdot)\)	520.bv	6	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{520}(31,\cdot)\)	520.s	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(1\)
\(\chi_{520}(33,\cdot)\)	520.cw	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{520}(37,\cdot)\)	520.cj	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{520}(41,\cdot)\)	520.ch	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{520}(43,\cdot)\)	520.cs	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{520}(47,\cdot)\)	520.v	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{520}(49,\cdot)\)	520.bz	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{520}(51,\cdot)\)	520.o	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{520}(53,\cdot)\)	520.ba	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(1\)
\(\chi_{520}(57,\cdot)\)	520.w	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{520}(59,\cdot)\)	520.cz	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{520}(61,\cdot)\)	520.by	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{520}(63,\cdot)\)	520.ck	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{520}(67,\cdot)\)	520.ci	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{520}(69,\cdot)\)	520.bp	6	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{520}(71,\cdot)\)	520.da	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{520}(73,\cdot)\)	520.w	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{520}(77,\cdot)\)	520.bg	4	yes	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{520}(79,\cdot)\)	520.n	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{520}(81,\cdot)\)	520.q	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{520}(83,\cdot)\)	520.x	4	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 192 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.